A finite element stress analysis of a crack in a bi-material plate

A stress analysis is presented for the problem of a crack in one material of a bi-material plate located perpendicular to the material interface. A numerical solution using the finite element techniques to determine the force displacement relationships is used. Knowing this, a work integral method is used to determine the stress intensity factors for the crack. Since the work integral is independent of path, the path of integration can be chosen far enough away from the crack tip to avoid the complications of the crack tip singularity. The problem is studied for a number of cases where the crack length to plate width ratio, distance from crack tip to material interface, and the ratio of material constants were varied as parameters.